Mermin comments on the “bad habit of physicists to take their most successful abstractions to be real properties of our world.” He starts with commenting on the reality of the quantum state:

[T]he recognition that quantum states are calculational devices and not real properties of a system forces one to formulate the sources of that discomfort in more nuanced, less sensational terms. Taking that view of quantum states can diminish the motivation for theoretical or experimental searches for a “mechanism” underlying “spooky actions at a distance” or the “collapse of the wavefunction”—searches that make life harder than it needs to be.

He then goes on to distinguish between the real and the abstract on the example of quantum field theory

I hope you will agree that you are not a continuous field of operators on an infinite-dimensional Hilbert space. Nor, for that matter, is the page you are reading or the chair you are sitting in. Quantum fields are useful mathematical tools. They enable us to calculate things.

and the spacetime continuum

[S]pacetime is an abstract four-dimensional mathematical continuum of points that approximately represent phenomena whose spatial and temporal extension we find it useful or necessary to ignore. The device of spacetime has been so powerful that we often reify that abstract bookkeeping structure, saying that we inhabit a world that is such a four- (or, for some of us, ten-) dimensional continuum.

He warns of the consequences of mistaking abstractions for reality

So when I hear that spacetime becomes a foam at the Planck scale, I don’t reach for my gun. (I haven’t any.) But I do wonder what that foam has to do with the macroscopic events that spacetime was constructed to represent and the macroscopic means we use to locate events.

Quantum mechanics has brought home to us the necessity of separating that irreducibly real experience from the remarkable, beautiful, and highly abstract superstructure we have found to tie it all together.

I completely agree with Mermin. One shouldn't mistake mathematical tools for reality, and mixing up both leads to confusions. Our task as physicists is to explain observations and make predictions for experiments, not to unravel the fundamental nature of reality (wink, wink). However, one should not throw out the baby with the bath water. We have a clear goal, but no map telling us how to get there. And while some might find the philosophy of science a waste of time, and others might say taking abstractions too seriously only creates artificial problems, these considerations could contain the clue, or the inspiration, necessary for progress.

Thus, while I personally am not too enchanted by taking maths to be reality, I think one should not simply dismiss these studies on the basis of gut-feeling. I was therefore put off, not by the actual opinion Mermin expressed, but by it being uninsightful, and - in its polemic way - potentially counterproductive by encouraging shallow argumentations.

“I hope you will agree,” David Mermin writes, “that you are not a continuous field of operators on an infinite-dimensional Hilbert space. Nor, for that matter, is the page you are reading or the chair you are sitting in.” His comment is a nice example of the logical fallacy known as “appeal to belief”: Most people believe X is true, so X is true. That many people believe they are not operators in Hilbert spaces, believe they do have free will, or do or don’t believe in global warming makes no difference as to whether a statement is true or false. I have no basis on which to decide what I “really” am. And though I personally think any such argument is a waste of time because it can never be decided anyway, and though I am sympathetic to the opinion Mermin expresses, his article dismisses the relevance of both quantum foundations and the philosophy of science out of hand in a rather polemic and not very insightful way.

Sabine HossenfelderWaterloo, Ontario, Canada

To which Mermin replies

Sabine Hossenfelder takes my rhetorical flourish as an attempt to argue, fallaciously, for the truth of that proposition. That was not my intent any more than I intended, by calling attention to the agreement among most of us that the ether is not real, to establish thereby its unreality. Although Hossenfelder takes my column as a shallow, polemical dismissal of both philosophy of science and quantum foundations, I had viewed it as an amateurish attempt to contribute to both disciplines.

It leaves me to wonder though why Physics Today prints such amateurish attempts. It's like opening a journal on medicine and reading a column proclaiming talking is a bad habit since, I hope you will agree, the human body is not made of words. And then find it explained as being an amateurish contribution to psychology.

In any case, I will now go act on some wave-functions.

“Philosophy is the talk on a cereal boxReligion is the smile on a dogI'm not aware of too many thingsI know what I know, if you know what I mean

75 comments:

Sorry, on the basis of the paragraphs you quoted I think it sounds like a well-written piece and I think you were too hard on the guy.

The first paragraph starting "The recognition that quantum states are calculational devices and not real properties of a system" makes a good point.

The second paragraph (which you objected to) starting "I hope you will agree that you are not a continuous field of operators" seems quite humble to me, the phrase "I hope you will agree" being quite carefully chosen so as not to be polemic. Though I would agree with you that we might never be able to tell what we really are, I do not think it is unreasonable to believe I am not a human-invented "continuous field of operators". Even though I do not know what I am, there are many things that I don't think I am.

Anyway, you were both basically in agreement. It sounds an interesting piece and it's a shame it's subscription only.

Truth be told, you are right, it's a well written and entertaining piece that has successfully stimulated some discussion. It's an interesting topic which is why I've reproduced it here. I continue to find it odd though to offer an argumentat on the basis of what somebody hopes somebody thinks in a science magazine. Best,

It is very silly to think that successful abstractions have nothing to tell us about the actual nature of reality.

For example can anyone seriously claim that the model describing Earth as revolving around the Sun is just a mere mathematical tool?

Good physical theories can tell us a lot about underlying reality the problem is that standard model of particle physics is not a good theory. It's a mess, a mix of good and bad ideas which just happen to agree with experiments but no one has any idea why. To me it's much more an engineering theory then a physical theory as it doesn't offer any deep and consistent insight it only offers prescriptions on achieving practical results. Unlike general relativity it's not a product of deep understanding it's a product of brute force attack - guessing equations and comparing them with data until the one which fits is found.

It is obvious to me that there exist a self consistent rational theory which successfully combines QM and gravity and explains much more then SM does while at the same time avoiding all of it's problems and contradictions - we simply haven't discovered it yet, once we do it will tell us a great deal about the actual nature of reality.

The problem is if you take a good theory and believe its ingredients to actually be, rather than describe, reality, you're maneuvering into a dead end. You can't improve the nature of reality, but you can improve a theory, and that might necessitate overthrowing the picture of reality former theories created. Best,

While I have no sympathy for "the world is mathematics" etc, one has to be careful. For example, Mermin seems to think that spacetime consists of "structureless points", but it doesn't. The modern definition of a manifold doesn't by any means forbid the points of the manifold to have a structure; think of the bundle of orthonormal frames over a Riemannian manifold, where each point is itself a very complicated object. Spacetime really *is* the set of all events --- the "points" are enormously complicated objects like "the assassination of JF Kennedy", "the birth of S Hossenfelder" etc etc. The fact that we often talk as if events were like Euclidean points doesn't change this fact.

[T]he recognition that quantum states are calculational devices and not real properties of a system forces one to formulate the sources of that discomfort in more nuanced, less sensational terms.

This may be more correct, but I think, less productive. I think Planck thought his quanta were computational devices necessary to produce the blackbody radiation curve. (Wiki) ""a purely formal assumption ... actually I did not think much about it..."" "for this reason, the philosopher and historian of science Thomas Kuhn argued that Einstein should be given credit for quantum theory more so than Planck, since Planck did not understand in a deep sense that he was "introducing the quantum" as a real physical entity."

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Real physical entity? No, a calculational device and not a real property of a system!

---Unrelated question - is the radio wave emitted by your cellular phone classical in the same sense that a billiard ball is? That is, we don't see a billiard ball in a superposition of states presumably because it is entangled with the environment, and quantum mechanical phase information is lost. Does the same hold for the classical electromagnetic field?

I'd argue that you definetly can interpret quantum states (eigenstates of the Hamiltonian operator) as physical and not just as a mathematical abstraction. Are the eigenstates of your room as an acoustic system just a mathematical abstraction?

In my own perspective Mermin is taking on the role of one of the prisoners in Plato’s cave rather than one whose mission is to free them. As far as I can see, it as if he is saying it is simply too painful and potentially dangerous to look into the light and as such better to be avoided.

And if there were a contest, and he had to compete in measuring the shadows with the prisoners who had never moved out of the cave, while his sight was still weak, and before his eyes had become steady (and the time which would be needed to acquire this new habit of sight might be very considerable) would he not be ridiculous? Men would say of him that up he went and down he came without his eyes; and that it was better not even to think of ascending; and if any one tried to loose another and lead him up to the light, let them only catch the offender, and they would put him to death. -Plato - The Allegory of the Cave

Arun: Depends on what you mean with classical. In contrast to billiard balls, you can easily do interference with electromagnetic waves. That in itself however isn't a quantum effect, it only is if you know the wave is "made" of particles.

I can't for the life of me see what Mermin wants 'reality' to mean. Is he a Platonist? Does he think Reality can be directly accessed by us in any way? If not by scientific means, then how - by the senses? By the imagination?

Until he makes his mind up what can or can't be real, there is not much point in him telling us that physical models are or aren't.

I think there is an extra (unwritten) line in physical theories that differentiate them from mathematics: something like 'The entities in this theory do exist and their properties must correspond to measurable ones (so far as they are measurable)'.

Then it is a question of whether the theory holds up against real measurements or not.

You can't test a physical theory at all without first making the assumption that it ought to describe (some part of) reality. Why would we bother building theories at all if they must all be (by Mermin's definition, whatever that is) unreal?

I suspect Physics Today allowed Mermin to write this thin pea-soup of an article because he is quite famous and the author of a good textbook...

I tend to agree with the philosopher Bergson when considering that a problem always have a solution that it deserves as a function of how it is stated as a problem, of the available conditions and terms to establish it as a problem (see also Deleuze's interpretation of Bergson).

Physics is the "problem" of describing nature. It has been noticed that this problem can be stated very precisely using mathematics. On the other hand, there is also the "problem" of what nature is "in fact" -- its "reality" (and even if there is one at all). Again, the solutions for this "problem" comes as a function of how you state it. Both "problems" are certainly constrained by how the human mind works.

So here are two great "problems" -- the "mathematical universe" and "reality" -- and their possible solutions (in terms of rational understanding -- or even the possibility of their ultimate conciliation) which are highly interpretative.

I would say that the arguments raised by Mermin's article focus on a somewhat simple dichotomy (physical reality versus mathematical tools) which misses all the grey scale between the two, which has to do with the nature of posing a "problem". It is a philosophical and deep issue that is not simple at all.

Definitely, these "problems" are mysteries that possibly have no answer under the way that they are currently formulated.

I'm rather more fond of thinking of myself as a state in the said infinite dimensional Hilbert space. Or, even more precisely, a whole subspace, with the extra freedom reserved for the parts of the universe that don't affect my sense of self.

Mermin said that "quantum states are calculational devices and not real properties of a system", and that "searches for a 'mechanism' underlying 'spooky actions at a distance' or the 'collapse of the wavefunction'—searches that make life harder than it needs to be" are a bad habit. If I would summarize, his view is that we should be happy to predict probabilities, without being concerned with explaining things. I agree that it is useful to predict probabilities, but we also want to have a description and understanding of reality as good as we can. We know that our descriptions may be not isomorphic with the reality, but why should we be concerned only with the operational approach? I think that Mermin objects here to searching for explanations. If Physics is only about predictions, then maybe we need a new science, concerned with explanations. But I was always thinking that the accurate predictions come from good explanations.

Thus far physics as you say has only been able to define reality reliably through mathematics. However, I would challenge that somewhat, as to turn it around if you will. As for instance for centuries it was widely accepted among physicists that nature had a tenancy to be both efficient and beautiful, which was later expressed as having conservation and symmetry being fundamental principles of nature and yet not understood for why that would necessarily be so.

Then along comes Emmy Noether, who demonstrates mathematically that for every symmetry, there is to be found a corresponding conserved quality/quantity and vice versa. The question this poses, is does this tell us anything more or reveal a greater truth about nature that had not been known, since even millennia before?

Thus my way own of looking at this is understand that mathematics is but one way we have discovered to be able to express logic and reason, with simple language being another. So for me it only serves to reinforce that nature and with it reality to be a structure of logic indicative of reason, for which we have found ways and likely to discover others by which it might be further described as to be understood.

Personally, I think we all are fundamentally a bunch of ones and zeroes and the information attached to those ones and zeroes is built-in so deeply you can't separate it from the ones and zeroes in any way.

I do think that article comes across as too against deep thinking though I do agree it's a great topic to bring up.

His response almost makes it seems like he's trying to be an amateur troll to start a good discussion which is odd. Could maybe be an interesting literary technique if he actually had something more profound to say later in the discussion.

Edie Brickell's sound went deep no matter how strongly a lyric might seem to want to stay shallow.

"(...)physics as you say has only been able to define reality reliably through mathematics."

Well, that was not exactly what I said. I wrote:

Physics is the "problem" of describing nature. It has been noticed that this problem can be stated very precisely using mathematics.

To "define reality" is quite different from "to describe nature" (nature in the sense of physical phenomena).

I emphasized a deep limitation that every problem invites a "solution that it deserves" and stated that the "two problems" mentioned by the author, namely, the fact that "physics can describe nature through mathematics" and "what is reality" require solutions as limited as the way their problems are posed, to begin with.

In the post in question, the author formulated those two problems as a simple dichotomy -- "mathematics" at one side, and "reality" at the other ("not to be confused one with the other", as his main message), whereas in fact I point to a much deeper difficulty. I hope this clarifies a bit.

Concerning symmetry principles, they are often stated mathematically in physics problems anyway, even though they may have a more subjective motivation.

“Personally, I think we all are fundamentally a bunch of ones and zeroes and the information attached to those ones and zeroes is built-in so deeply you can't separate it from the ones and zeroes in any way.”

There are many who believe there is nothing to reality that extends past the mathematics, which you express as the ones and the zeros. Yet in our every day experience these only account for the way things are arranged or ordered if you will.

However, one must still have things of material that are to be so ordered for which those ones and zeros to be represented physically to have a reality. For me it has never been hard to imagine that there indeed must be and have always been things, yet more difficult to understand why they in being must also need to be ordered? In my way of thinking physics takes for granted what is being ordered, while attempting to understand in what way and perhaps even why this is necessarily so.

To be able to define as opposed to being able to describe posing as being a difference is one that I must admit at present escapes me. However I must also confess to have never read Bergson and probably should refrain from making comment until his message be given a chance to percolate through by way of having remedied that:-)

To define is to establish exactly the nature or character of something; to describe is to give the relevant characteristics or behavior of something. When describing, it is not immediately evident that you get something exactly defined.

Also, notice that in my previous comment there is also a difference between the words "reality" and "nature"; the latter refers to the "physical world", the realm of all that can be objectively measured; the former is much more difficult to define, but for realists it could be seen as the ultimate or fundamental constituints of nature, so that the latter is just but a level of the former.

Just as a follow up question as to clarify, if I were to say that "a circle is the set of points in a plane that are equidistant from a given point" or on the other hand “a circle is the boundary formed that is the smallest possible for any given area to be contained” which would you render as being a description and which as a definition?

The words definition and description were not meant in my original comment to be taken under formal mathematical terminology, but more generally, in the sense of my latest comment. So to answer your question, both are "definitions". (Under mathematical terminology, the latter happens to be a theorem, the isoperimetric theorem).

The statement that quantum states are just calculational devices and not real properties of a system is not a deep one, as Max Born pointed out many times. 'Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and objective?' [Max Born]

What you say is true within the limits you have imposed, yet for me both are indistinguishable as being either a description or definition as except the latter being an imposed conservation and the former simply one method by which you could identify and confirm its presence or symmetry if you will. The reality of course is the existence of the circle itself. Then again perhaps there is something that eludes me and as I said maybe Bergson might have this become more evident.

Theories are constructed by humans for humans and we are doomed to use concepts that can be understood and conceived by our minds. We are doomed to make approximations; Mathematics like any other language has limitations to what it can express and we contact experiments based on our intuitions and our theories; we measure what we want to measure and the reasults have a meaning for us. We can't escape ourselves and our notions are *our notions*. But that's fine. This is our Cosmos and the only Reality is our reality; it can't be otherwise.

The difference between definition and description has nothing to do with the reading of Bergson. I only invoked Bergson from the idea that "a problem always have a solution that it deserves as a function of how it is stated as a problem, of the available conditions and terms to establish it as a problem".

As for the difference between the two terms, I fail to see why they are equal, but never mind.

I didn’t really mean for this to run off as being one of those how many angels can fit on the point of a pin discussions, yet given your criteria which of the two statements I made would be considered as a definition and which a description? As follow up which if any of the two do you find to be the most significant as it relates to coming to grips with what reality is?

If something can be defined, then it can always be described. But the reverse is not necessarily true. Example from physics:

Define "light".

You can describe it from the classical or quantum points of view (theories) using mathematical expressions for the description of light phenomena. Notice that these are *not* definitions of light, but mere descriptions of phenomena. From these descriptions it is not necessarily true that you have a definiton of light in the sense that you have a *complete* objective characterization and understanding of it, its true nature (This can be challenged as well -- is there a "true nature" in all things?. This is often the case for philosphy of science to ask the true meaning of "photon", its ontic status, etc).

Of course, you can "define" light a priori and evaluate afterwards all the consequences of your definition and see if your definition is compatible with the light phenomena. Your definition is then like a postulate. But even though this can lead to deep insights, it is just an operational definition, it does not mean that the true nature of light is understood, so you do not have actually a definition of it.

I like what you said here and it has had me to understand you point more precisely. So we could say that a definition is the essence of something real, while a description is the exposure of some aspect or consequence of its being real. I can accept this such that we then find all theories as being descriptions, rather than definitions. However, this leads one to ask is there anything that can be called or assigned as an actual definition, when they can only be approached by way of how they may be described? I think we must let go of this, as to say for instance. that light is what denies there being darkness and then proceed on from there.

It's very difficult to define what makes things real because we seem to employ very circular definitions of what is real - we define real things in terms of objects we already consider real. For example, "I know the apple is real because I can hold it in my hand". So we define the real-ness of the apple on the basis of the assumed real-ness of our hand. Because we can touch it, we say it is real. But that's a very circular definition. Likewise with light, we would say "I know the light is real because it illuminates the book". That circular definition seems to be the best definition we have.

Just as a follow up question as to clarify, if I were to say that "a circle is the set of points in a plane that are equidistant from a given point" or on the other hand “a circle is the boundary formed that is the smallest possible for any given area to be contained” which would you render as being a description and which as a definition?

Both are definitions, the equivalence can be proved. But that is the nature of mathematics. That feature of mathematics is generally not shared by the real world. The equivalence of two such statements in the real world can generally be made only in the context of some theory, which could be overthrown anytime.

My example had nothing to do with the number of angels on the head of a pin. It has to do with the difficulty anthropologists, etc., have in including various practices in various cultures under the rubric of "religion".

I guess this is where I differ with both you and Christine, for the equivalency you site does not have them to be the same yet merely related. The former I see as being a description, as it tells us how we might construct a circle without any thought as to how it can serve reality in terms of its existence, while the latter lends one insight into the utility or the purpose of a circle if you will and I find it closer as serving well as being a definition.

The same for me is what I see as the difference between conservation and symmetry, where symmetry can only lend description of how to achieve the required implications or consequence of the other. Perhaps for many this may seem as a somewhat simplistic and naive point of view, yet it allows me to tell the difference from what is called phenomena and what might be considered as a means to identify what has things to be considered real.

From AWT follows theorem "Simmilia simillibus observatur". Every observer, which is formed by some particular density fluctuation of chaotic field would see only these density fluctuations from his neighborhood, which are somewhat similar to him.

In such a way, mathematician would see his universe formed by numbers, quantum mechanist would see universe indeterministic by its very nature (note that these two perspectives are mutually exclusive) and aetherist would see Universe composed of inertial particles.

Because we cannot remain very same persons, our vision of Universe can never become universal as well. Every of us is living in its own version of multiverse. We can understand Universe well only if we can reproduce thinking of other people about it.

"The recognition that quantum states are calculational devices and not real properties of a system". The great physicist J.Schwinger once wrote : " Quantum mechanics is a symbolic expression of laws of microscopic measurement ".

Under the heading of Mathematics, it seems you can ask the same question as to whether Mathematics was "Invented or discovered." Yet, still under the heading of mathematics, ask whether the mathematics is a good description of the reality?

João Magueijo started reading Einstein when he was 11, but he wanted to comprehend the theory using mathematics rather than words. So he read a book by Max Born, which explains relativity in the language of mathematics. He quotes Galileo as having said, "The book of nature is written in the language of mathematics."

"Einstein's Bovine dream" is always a good reminder of how one views "jumps in relation too ..... Magueijo and Faster then the speed of light.

Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1).See: Mathematical Problems of David Hilbert

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For the advancing army of physics, battling for many a decade with heat and sound, fields and particles, gravitation and spacetime geometry, the cavalry of mathematics, galloping out ahead, provided what it thought to be the rationale for the real number system. Encounter with the quantum has taught us, however, that we acquire our knowledge in bits; that the continuum is forever beyond our reach. Yet for daily work the concept of the continuum has been and will continue to be as indispensable for physics as it is for mathematics. In either field of endeavor, in any given enterprise, we can adopt the continuum and give up absolute logical rigor, or adopt rigor and give up the continuum, but we can't pursue both approaches at the same time in the same application.

I read that issue of Physics Today and was wondering when you were going to blog about it. Thanks for expanding on your interesting letter to Mermin.

But I really liked your reply to Arrow: "The problem is if you take a good theory and believe its ingredients to actually be, rather than describe, reality, you're maneuvering into a dead end. You can't improve the nature of reality, but you can improve a theory, and that might necessitate overthrowing the picture of reality former theories created."

Under the heading of Mathematics, it seems you can ask the same question as to whether Mathematics was "Invented or discovered."

I think that physics itself lends credence to the view that mathematics is a discovery, rather than an invention. For instance, you can take my example of the circle and extend it to the sphere, to say that a sphere is the boundary formed that is the minimum required to enclose any given volume. So when we look to the heavens to see the planets and stars to have taken on on such a shape, would it be reasonable to say this was not decided upon until the invention of mathematics? It would also be fair to ask whether those stars and planets are in themselves the essence of reality or rather the form which they had no choice other than to assume. So we find ourselves back to this distinction between description and definition wondering what can serve to differentiate between them.

Now that I've came across the original article I have to say that to me it reads a lot like an old man trying to come to terms with his failure to make sense of QM. He has apparently given up and now attempts to get rid of the cognitive dissonance by convincing himself and others that there is no problem to begin with.

He argues that taking seriously questionable parts of the formalism "makes life harder then it needs be," and that one can simply disregard the implications one finds troubling since it's merely a mathematical tool.

This is nonsense and the distinction between the reality and it's description has nothing to do with it. Even if QM is merely a mathematical tool there is no doubt that certain properties of the actual reality are encoded in it since it correctly predicts experiments. Since we don't know which parts mirror reality and which are just an unnecessary baggage we have to afford the same importance to them all. (It could even be argued that problematic parts are more important since they can potentially lead us to better solutions)

To use his example the fact that QM is just a mere mathematical tool doesn't make spooky action at a distance (SAD) any less of a problem. Such thinking would only be warranted if SAD were proven to be an unnecessary baggage and not a part crucial to correctly describe reality. Such a proof however can only be made by reformulating the theory without SAD and showing that it still agrees with experiments.

All in all the article is full of defeatism. I may be harsh but I see this attitude all too often and believe it is very harmful to progress in physics.

PS. Google '"What's bad about this habit" filetype:pdf' for the article.

The "spooky action on a distance" in itself is already an interpretation, so one has to be careful with what the alleged problem is. Which is essentially what I meant to say, you don't make progress with taking abstractions for reality, but you don't make progress with throwing out the puzzles they bring either. Best,

While I don't argue that appeal to intuition is no way to do physics, people do often forget the difference between mathematical and physical space, and I think that does sometimes hold back scientific thinking.

We do sometimes put more faith into the tools that we have created than we should, and even seem to feel hesitant or guilty to modify them when evidence suggests that we should. People do need to remember that mathematics is a human creation. While it is incredibly powerful as a tool, it is still just a tool. Now, that doesn't mean that results/interpretations should be dismissed because they are only expressible in terms of these created mathematical objects, but that when doing physics, there should be a thought somewhere in the back of your mind that the mathematical space is not the same as the physical space - in my opinion, at least.

classical space-time emerges from quantum one when discontinues, ie. measurement jumps are "smoothed"(in mind), and so you have the illusion that time is continuous. perception is too slow to catch these discontinuities, like the eye is too slow to notice that movies are really set of stills that exchange at a rate of about 24 frames per second.nv

The lessons of history are clear. The more exotic, the more abstract the knowledge, the more profound will be its consequences." Leon Lederman, from an address to the Franklin Institute, 1995

Hi Phil,

You wrote:I think that physics itself lends credence to the view that mathematics is a discovery, rather than an invention.

This would fall in line with my perspective as well. I mean we are certainly looking at nature and finding "elements of it" according to science principles, so why would you not understand that you are in essence explaining nature "to a degree?"

Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment." K. Shumacker

So you know about my fictional mining company and the land I claimed on the moon? Well, I had to give consideration to what would transpire from any planet's isostatic adjustment and it's unique formation?:)So why not direct an object for collision on the moon, for elemental examination?:)

Geometrically the sphere is a leading perspective and inverse square law, it's applicability. Spherical cows, on cosmological perspective.

Let us see how geometrics have historically progressed from what Einstein learnt from Grossman about Riemann's geometry??

One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean.On Gauss's Mountains

Now we understand well that Grace measures the earth in ways that LIGo "might manage gravitational disturbances across a beam of light?"

Quantum mechanics is better off as a branch of mathematics rather than physics! Physicists have been debating for decades about quantum mechanics , without any general consensus.So it may be time to give an abstract axiomatization that brings quantum mechanics close to pure mathematics in Hilbert`s spirit!

It seems to me the author in question is pushing defeatism as a good philosophical stance for quantum physics, as Arrow stated. The author makes broad sweeping generalizations, such as suggesting that there will never be something that stands in for the original ether. I believe there is a real and physical collection of quantum spaces that are point-like. However, unlike the original ether it has no inertial reference frame and only responds to acceleration. That simple change from the original inertial framed ether has been what has stymied progress in coordinating quantum physics with gravitational physics.

It seems to me theoriticians are too quick to find a dead end in one particular area of physics and then broaden the idea IN THEIR OWN MINDS to parts of physics that are really unrelated. Whole areas of physics which had an original intuitive component are then simply shut down because just one major component of the system was a dead end.

In my view they are both, as the puzzle itself being an invention. Yet with the rules that govern it being logic as expressed through mathematics being discoveries.

” In addition, there are no planets or stars that are spheres. It so happens that their globular shape can be well-approximated by a sphere, but that is a mathematical idealization.”

Yes most definitely they are not perfect spheres, which is in itself can and does serve as being revealing. That is in asking why, one may discover there are other actions at work, such as those of angular momentum. That’s to say if all we were given is a still photo of a planet or star, we could surmise that it is not sitting motionless within the void yet actually rotating. Of course the mystery still remains, which Newton first had to be made evident, which is to ask what is it rotating relative to? :-)

Although I am certain I don’t share the power of intellect with those like Roger Penrose, the one thing I do have in common is to admit to being unashamed Platonist. Also, I share the sentiment expressed often by Penrose as to being somewhat mystified as to how in being a reductionist could lead many of his colleagues to believe there is no underpinning truth(s) to either nature or reality, as in essence that is what they are counting on to discover and in doing so able to make predictions from attaining such insight. In short it is to ask why a person who believes there be to be no underlying order to reality would ever aspire to becoming a physicist.

One of my favorite quotes from Weinberg's "Dreams of a Final Theory" is in the anecdote about the erstwhile promising grad student who mysteriously dropped off the map. Weinberg asks his colleague what happened, and he sadly replies "He tried to understand quantum mechanics."

From this outsider's perspective, the problem with quantum philosophy appears to be that it can be rather counterproductive, even perilous. People get sucked into these insoluble arguments about what is real or not, and yet every "solution" to the "problem" involves complicating the interpretive model with something that not only yields results that are indistinguishable from any other model, but have parts that can never be observed. Ever. I simply fail to see the point in that. I don't understand why "determinism" or "local reality" are so worthy of anguish when, time and again, the energy spent making "sense" of it all yields precisely nothing of practical utility.

The only (faint) hope that am only aware of are these "brownian" sorts of models, positing a microscopic sub-quantum layer of reality, in which quantum weirdness is something that evolves out of the jiggling of these little bits of whatever (preons?), but is fundamentally entirely deterministic. I think these models predict that quantum computation has a physical, vs. practical, limit not predicted by quantum mechanics. Trouble is, if I understand correctly, this limit is presently safe from science, as it would require an ensemble of entangled particles that is so large it is well beyond our grasp, making this model completely indistinguishable from decoherence. Do I understand correctly here? If so, again, I ask, after literally 100 years of bashing quantum mechanics for its incomprehensibility or whatever other human value it appears to violate, has anything remotely useful come out of the trouble?

In quantum teleportation, complete information about the quantum state of a particle is instantaneously transferred by the sender, who is usually called Alice, to a receiver called Bob. Quantum superposition, meanwhile, allows a particle to be in two or more quantum states at the same time

As your Sudoku puzzle I would say the light bulb stands as being both invention and discovery , as the idea for it sprang from the imagination of a human mind, working within the bounds and possibilities as they exist in the reality of the world. You could say this is what emergent phenomena stands as being, in having things reaching a potential innate as a consequence of the environment in which it was able to form. Simply put resultant of things forming out of potential, with having potential ignored for being mainly as simply an abstract notion rather than the vital aspect of reality it actually stands and has so often demonstreated to be.

“But this is certain, and an opinion commonly received among theologians, that the action by which he now sustains it is the same with that by which he originally created it; so that even although he had from the beginning given it no other form than that of chaos, provided only he had established certain laws of nature, and had lent it his concurrence to enable it to act as it is wont to do, it may be believed, without discredit to the miracle of creation, that, in this way alone, things purely material might, in course of time, have become such as we observe them at present; and their nature is much more easily conceived when they are beheld coming in this manner gradually into existence, than when they are only considered as produced at once in a finished and perfect state.”

- René Descartes - Discourse on The Method: of Rightly Conducting The Reason, and Seeking Truth in the Sciences (1637)

One of my favorite quotes from Weinberg's "Dreams of a Final Theory" is in the anecdote about the erstwhile promising grad student who mysteriously dropped off the map. Weinberg asks his colleague what happened, and he sadly replies "He tried to understand quantum mechanics."

To me the problem is that there is no systematic exposition of the bizarreness of QM. It seems more like a collection of clever ideas. I don't care about the "interpretation of QM". I want a systematic - almost Euclid's geometry-like - way of exhibiting these.

What is troubling also is that perhaps QM is too wierd to arrive at without lots of experimental guidance. What if the next theory is weirder yet?